The kernel for the budget is monotonic based on the assumption on the performance vs budget (Eq. (7))
The budget kernel reduces the necessity of inferring the similarity between tasks
Acquisition function (AF) is PES/cost
Most parts overlap with the propositions in the MTBO paper, but this paper modifies the cost to include the BO inference time and the kernel for the budget.
The experiment uses the budgets of $\{1/64,1/32,1/16,1/8\}$
Not a main point, but the paper well-explains the algorithm of entropy search.
Experiments
The authors used a bunch of self-made benchmarks.
Performance over time
x-axis: runtime (log-scale, second)
y-axis: loss
Fabolas
MTBO with a meta-task from a bunch of different dataset size
Expected improvement (EI)
Entropy search (ES)
Hyperband (HB)
random search
Various different self-made benchmarks (but probably, I saw them in the A-BOHB (ABOHB) paper)
Fast Bayesian hyperparameter optimization on large datasets
FABOLAS paper.
Main points
Not a main point, but the paper well-explains the algorithm of entropy search.
Experiments
The authors used a bunch of self-made benchmarks.
Performance over time
x-axis: runtime (log-scale, second) y-axis: loss
Various different self-made benchmarks (but probably, I saw them in the A-BOHB (ABOHB) paper)